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Evaluate 5-\(^{3log_52}\) x 2\(^{2log_23}\)
The expression ax\(^2\) + bx + c equals 5 at x = 1. If its derivative is 2x + 1, what are the values of a, b, and c, respectively?
A function f(x) passes through the origin and its first derivative is 3x + 2. What is f(x)?
In how many ways can a delegation of 3 be chosen from among 5 men and 3 women, if at least one man and at least one woman must be included?
Find the sum of the range and the mode of the set of numbers 10, 9, 10, 9, 8, 7, 7, 10, 8, 10, 8, 4, 6, 9, 10, 9, 10, 9, 7, 10, 6, 5
The variance of x, 2x, 3x, 4x and 5x is
If U = {x : x is an integer and 1 \(\leq\) x \(\leq\) 20}
E\(_1\) = {x : x is a multiple of 3}
E\(_2\) = {x : x is a multiple of 4}
and an integer is picked at random from U, find the probability that it is not in E\(_2\)
Given that the various faces of a fair dice 1, 2, 3, 4, 5, 6 appeared 30, 43, 54, 40, 41, 32 times respectively in a single toss. Picture the figures as being represented in a simple table with number (X) against frequency (f).
If a pie chart is used to depict the data, the angle corresponding to 4 is?
In how many ways can the word MATHEMATICS be arranged?
If the mean of the numbers 0, (x+2), (3x+6), and (4x+8) is 4, find their mean deviation.
X and Y are two events. The probability of X or Y is 0.7 and that of X is 0.4. If X and Y are independent, find the probability of Y.
If the volume of a hemisphere is increasing at a steady rate of 18π m\(^{3}\) s\(^{-1}\), at what rate is its radius changing when its is 6m?
A bowl is designed by revolving completely the area enclosed by y = x\(^2\) - 1, y = 3, and x ≥ 0 around the y-axis. What is the volume of this bowl?
If y = 2xcos2x - sin2x, find \(\frac{dy}{dx}\) when x = \(\frac{π}{4}\)
Find the value of \(\int^{\pi}_{0}\frac{cos^{2}\theta-1}{sin^{2}\theta}d\theta\)
A predator moves in a circle of radius √2 centre (0,0), while a prey moves along the line y = x. If 0 \(\leq\) x \(\leq\) 2, at which point(s) will they meet?
In a regular polygon, each interior angle doubles its corresponding exterior angle. Find the number of sides of the polygon.
if P and Q are fixed points and X is a point which moves so that XP = XQ, the locus of X is
3y = 4x - 1 and Ky = x + 3 are equations of two straight lines. If the two lines are perpendicular to each other, find K.
An equilateral triangle of side √3cm is inscribed in a circle. Find the radius of the circle.